We introduce naive traders in bilateral trading. These traders report their true types in direct mechanisms and bid/ask their values/costs in auctions. We show that by expropriating naive traders in direct mechanisms, the mechanism designer can subsidize additional trades by strategic traders and improve efficiency. In fact, complete expropriation of naive traders is a necessary condition for constrained efficiency. A significant implication is that in the presence of naive traders, ex-post individually rational mechanisms are not constrained efficient. In contrast, if the traders must use a given mechanism, then the introduction of naive traders has an ambiguous effect on efficiency.